CAIE IGCSE Mathematics Extended E6.2 Right Angled Triangles Topic Practice

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Covered syllabus points

E6.2.1 Know and use the sine, cosine and tangent ratios for acute angles inE6.2.2 Solve problems in two dimensions using Pythagoras’ theorem andE6.2.3 Know that the perpendicular distance from a point to a line is theE6.2.4 Carry out calculations involving angles of elevation and depression

Question 1

[Maximum number: 11]

Question (a)

(a)
Figure for Question (a) — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

The diagram shows a right-angled triangle PQR on horizontal ground. X is vertically above R and the angle of elevation of X from P is 21∘21^{\circ}. XR=2.8 mX R=2.8 \mathrm{~m} and RQ=7.1 mR Q=7.1 \mathrm{~m}.

[ 5 ]

Question (i)

(i)

Calculate the angle of elevation of X from Q.

[ 2 ]

Question (ii)

(ii)

Calculate PQ.

[ 3 ]

Question (b)

(b)

Calculate the acute angle KML.

[ 3 ]

Question (c)

(c)
Figure for Question (c) — CAIE IGCSE Mathematics Extended

The area of triangle ABC is 62.89 cm262.89 \mathrm{~cm}^{2}.

[ 3 ]

Question (i)

(i)

AB is extended to a point D such that angle B D C=90^.

Calculate BD.
cm

[ 3 ]

Question 2

[Maximum number: 5]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

\section*{NOT TO SCALE}

The diagram shows a quadrilateral ABCD.
CD=10 mC D=10 \mathrm{~m} and DB=12 mD B=12 \mathrm{~m}.
Angle DBA=90∘D B A=90^{\circ}, angle CDB=56∘C D B=56^{\circ} and angle ADB=34∘A D B=34^{\circ}.

Question (a)

(a)

Calculate the length of AB.

[ 2 ]

Question (b)

(b)

Calculate the shortest distance from B to the line AD.

[ 3 ]
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